But the Blues boss admits he is likely to have wait until the end of the summer for a move for the Scottish international.
Appleton is keen on seeing Maguire back at Fratton Park in League One next season after impressing in his loan stay from Derby this term.
The 23-year-old bagged three goals in 11 appearances – including a stunner in the south coast derby at St Mary’s – and made himself a fans’ favourite with his all-action displays.
Appleton knows Championship sides will be keeping tabs on the Scot after he caught the eye at Pompey.
Maguire’s future at Pride Park looks bleak after he fell out of favour there under Nigel Clough.
Appleton is waiting to know exactly what budget he can work to, with Pompey still in administration and fighting to stay afloat.
But that isn’t stopping him planning ahead and holding meetings with prospective signings for next season.
The Pompey boss knows it would have to be a waiting game with Maguire – but believes it could happen.
Appleton said ‘I’ve not given up on him.
‘It’s going to be difficult because of what he did here with us.
‘I would imagine he’d get quite a few offers at Championship level.
‘If it did happen, it could be right at the end of the summer.
‘First and foremost, Derby need to rule him out of being part of their squad.
‘If that was the case, depending on the interest he had, it could happen.
‘It wouldn’t be a quick one.
‘Ultimately, I would probably be led by his agent on it.’
Appleton is continuing with his recruitment plans for next season, despite the uncertainty over Pompey’s future.
He has met with a number of players who would potentially fall into the heavily-reduced wage structure he will be operating on next season.
Barnet’s Izale McLeod is one person Appleton has been linked with.
The 36-year-old boss feels it is critical to have plans in place so he can quickly react when the way forward for the Blues becomes clearer.
Appleton feels he will be capable of tempting players to put pen to paper and join his Pompey vision for the future.
He said: ‘I’ve been all over the country trying to speak to players and get things sorted, so I don’t get caught on the hop.
‘As soon as it’s sorted the better for me so I can start physically putting it on the line with players.
‘Selling the potential here would probably be something I would use to sell the club to players who could get a Championship club.
‘If they are prepared to take 12 months out and be part of something which could be special for the next three or four seasons, that’s what I’ll be looking to do.’